Mastering Logarithms: Using the TI-84 and Change of Base

Algebra 2 Grades High School 1:35 Video
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Lesson Description

Learn how to evaluate logarithms with different bases using the TI-84 calculator and the change of base formula. This lesson covers both methods, ensuring you can solve logarithmic problems efficiently.

Video Resource

TI-84 TI-83 Finding Log Values

Mario's Math Tutoring

Duration: 1:35
Watch on YouTube

Key Concepts

  • Logarithms with different bases
  • TI-84 calculator log base function
  • Change of base formula

Learning Objectives

  • Use the TI-84 calculator to evaluate logarithms with different bases.
  • Apply the change of base formula to evaluate logarithms with different bases.
  • Understand the relationship between logarithms and exponents.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a logarithm and its relationship to exponents. Briefly discuss the challenge of evaluating logarithms with bases other than 10 or e.
  • TI-84 Log Base Function (10 mins)
    Demonstrate how to use the 'log base' function on the TI-84 calculator, as shown in the video (0:33-1:05). Guide students through the steps and provide examples. Have students practice evaluating various logarithms with different bases using their calculators.
  • Change of Base Formula (15 mins)
    Explain the change of base formula and its purpose. Walk through the example from the video (1:05 onwards), showing how to apply the formula using both common logarithms (base 10) and natural logarithms (base e). Emphasize that the choice of the new base doesn't affect the result. Provide additional examples for students to practice.
  • Practice and Application (15 mins)
    Provide a set of practice problems involving logarithms with different bases. Encourage students to use both the TI-84's log base function (if available) and the change of base formula to solve the problems. Discuss the advantages and disadvantages of each method.
  • Wrap-up and Q&A (5 mins)
    Summarize the key concepts covered in the lesson. Answer any remaining questions from students. Preview the next lesson on logarithmic equations or applications of logarithms.

Interactive Exercises

  • Calculator Challenge
    Students compete to solve a series of logarithm problems with different bases, using either the TI-84's log base function or the change of base formula. The first student to correctly solve each problem wins a point.
  • Group Problem Solving
    Divide students into small groups and assign each group a set of logarithm problems with varying levels of difficulty. Each group must work together to solve the problems and present their solutions to the class.

Discussion Questions

  • Why is it important to be able to evaluate logarithms with different bases?
  • What are the advantages and disadvantages of using the TI-84's log base function versus the change of base formula?
  • Can you think of real-world situations where logarithms with bases other than 10 or e might be used?

Skills Developed

  • Logarithmic calculation
  • Problem-solving
  • Calculator proficiency

Multiple Choice Questions

Question 1:

What is the value of log base 2 of 8?

Correct Answer: 3

Question 2:

The change of base formula allows you to convert a logarithm to a new base using which operation?

Correct Answer: Division

Question 3:

Which of the following is the correct change of base formula for log base a of b?

Correct Answer: log(b) / log(a)

Question 4:

Using the change of base formula with base 10, what is log base 5 of 20 approximately equal to?

Correct Answer: 1.86

Question 5:

If your TI-84 calculator does NOT have a log base function, what formula should you use to evaluate logarithms with different bases?

Correct Answer: Change of Base Formula

Question 6:

What is the base of the natural logarithm (ln)?

Correct Answer: e

Question 7:

What is the value of log base 3 of 9?

Correct Answer: 2

Question 8:

Evaluate log base 4 of 16 using the change of base formula with natural logs.

Correct Answer: 2

Question 9:

Which of the following is equivalent to log base x of y = z?

Correct Answer: x^z = y

Question 10:

Which button needs to be pressed on the TI-84 to access the Log Base function?

Correct Answer: MATH

Fill in the Blank Questions

Question 1:

The function on the TI-84 that allows you to directly input the base of a logarithm is called ______.

Correct Answer: log base

Question 2:

The change of base formula states that log base a of b is equal to log(b) / log(_____).

Correct Answer: a

Question 3:

If you don't have the log base function on your calculator, you can use the ______ to solve.

Correct Answer: change of base formula

Question 4:

The base of the common logarithm (log) is ______.

Correct Answer: 10

Question 5:

ln(x) represents the ______ logarithm of x.

Correct Answer: natural

Question 6:

Log base 7 of 49 is equal to ______.

Correct Answer: 2

Question 7:

The change of base formula can be used with any valid ______.

Correct Answer: base

Question 8:

When using the change of base formula the numerator should be the log of the ______.

Correct Answer: argument

Question 9:

Logarithms are the inverse of _______ functions.

Correct Answer: exponential

Question 10:

To get to the Log Base feature on the TI-84, you first press MATH, and then you select option ______.

Correct Answer: A

Educational Standards

A2.A.1.6:Solve common and natural logarithmic equations using the properties of logarithms. A2.F.1.4:Graph exponential and logarithmic functions. Identify the domain, range, asymptotes, and x- and y-intercepts using various methods and tools that may include calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.

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